Question

Let \( U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \} \), \( A = \{ 1, 2, 3, 4 \} \), \( B = \{ 2, 4, 6, 8 \} \), and \( C = \{ 3, 4, 5, 6 \} \), the number of elements in \( (A \cap C) - (B - C) \), where \( (A \cap C)' \) and \( (B - C)' \) are the complements of \( (A \cap C) \) and \( (B - C) \), respectively is:

• A. 0
• B. 1
• C. 2
• D. 4

Hint:

Always calculate set operations like intersection and difference step by step to avoid mistakes.

Answer 1

The Correct Option is C

First, find \( A \cap C = \{ 3, 4 \} \) and \( B - C = \{ 2, 6, 8 \} \), the elements of \( (A \cap C) - (B - C) \) are the elements in \( A \cap C \) but not in \( B - C \). So, the result is \( \{ 4 \} \), and the total number of elements is 2.